Current algebra functors and extensions

TL;DR

This paper explores how current algebra functors generate fundamental cocycles and extensions for current Lie algebras and symmetry Lie algebras in sigma models, linking algebraic structures with their group counterparts.

Contribution

It introduces a method to derive cocycles and group extensions from current algebra functors, connecting algebraic and geometric perspectives.

Findings

Derived fundamental cocycles using current algebra functors

Constructed current group extensions for Lie algebra extensions

Linked algebraic structures to geometric symmetries in sigma models

Abstract

We show how the fundamental cocycles on current Lie algebras and the Lie algebra of symmetries for the sigma model are obtained via the current algebra functors. We present current group extensions integrating some of these current Lie algebra extensions.